Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Computer and Information Science

First Advisor

Kostas Daniilidis


The aggressive resurgence of convolutional neural network (CNN) models for prediction has

led to new benchmarks in speech recognition, natural language processing and computer

vision. In computer vision, the success of these models is often attributed to the combination

of a highly nonlinear cascaded processing scheme and the equivariance of planar convolution

to translations of the input. This thesis introduces methods that extend the equivariance

capability of CNNs to linear Lie groups that describe: the motion of objects, the structure of

the Euclidean world and the formation of images. The first approach introduces a framework

for joint estimation of image and motion representations. The linear Lie group structure

is enforced through a bilinear motion model which transforms an image representation

by the linear combination of motion generators. The approach affords extrapolation of

image sequences through linear extrapolation of transformation coefficients. In the second

approach, 3D rotationally equivariant representations are learned by convolution of spherical

functions with respect to the 3D rotation group. Methods are described for the convolution

of functions on both the two- and three-spheres. The final approach enforces equivariance

of representations to 2D dilated-rotations by preprocessing the input with a change of



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